Articles

Ubiquity symposium 'What is computation?'
Opening statement

Most people understand a computation as a process evoked when a computational agent acts on its inputs under the control of an algorithm. The classical Turing machine model has long served as the fundamental reference model because an appropriate Turing machine can simulate every other computational model known. The Turing model is a good abstraction for most digital computers because the number of steps to execute a Turing machine algorithm is predictive of the running time of the computation on a digital computer. However, the Turing model is not as well matched for the natural, interactive, and continuous information processes frequently encountered today. Other models whose structures more closely match the information processes involved give better predictions of running time and space. Models based on transforming representations may be useful.

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"So, what is the problem with the Turing model? To many,
the Turing machine model is a poor representation of the systems
they are interested in. For example, a DNA molecule being
transcribed does not resemble a moveable control unit on an
infinite tape. The theorems about running times of algorithms on
Turing machines do not help mathematicians solving continuous
models predict the running times of their models".
You have my permission to abandon the Turing Machine model and replace
it by anything else which works for you.
But I am guessing that "a DNA molecule being transcribed" is modelled
quite well by "a moveable control unit on an infinite tape".
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"The theorems about running times of algorithms on
Turing machines do not help mathematicians solving continuous
models predict the running times of their models".
I agree that it may turn out to be impractical to use a Turing machine for serious work. But isn't it a simple model of a CPU with an absurdly
inefficient storage device (similar to magnetic tape, which was in
fact used widely in the 1970's).
There is nothing to stop a new Ken Thompson from inventing a new
machine. It will be describable as interacting finite state
machines, and therefore it will be describable as
interacting Turing machines. Maybe you could leave out the infinite
tape, and replace it by ports which can store input and output
from other devices.